LMFDB - Embedded newform 1638.2.m.b.1621.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1638.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.m (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1638.1621
Dual form			1638.2.m.b.289.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.00000 - 1.73205i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-3.50000 - 0.866025i) q^{13} +(2.50000 + 0.866025i) q^{14} +1.00000 q^{16} +4.00000 q^{17} +(-2.50000 + 4.33013i) q^{19} +(1.00000 + 1.73205i) q^{20} +(1.00000 + 1.73205i) q^{22} +2.00000 q^{23} +(0.500000 - 0.866025i) q^{25} +(3.50000 + 0.866025i) q^{26} +(-2.50000 - 0.866025i) q^{28} +(4.00000 - 6.92820i) q^{29} -1.00000 q^{32} -4.00000 q^{34} +(-1.00000 - 5.19615i) q^{35} +7.00000 q^{37} +(2.50000 - 4.33013i) q^{38} +(-1.00000 - 1.73205i) q^{40} +(5.00000 - 8.66025i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(-1.00000 - 1.73205i) q^{44} -2.00000 q^{46} +(6.00000 + 10.3923i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-3.50000 - 0.866025i) q^{52} +(3.00000 - 5.19615i) q^{53} +(2.00000 - 3.46410i) q^{55} +(2.50000 + 0.866025i) q^{56} +(-4.00000 + 6.92820i) q^{58} +(0.500000 - 0.866025i) q^{61} +1.00000 q^{64} +(-2.00000 - 6.92820i) q^{65} +(4.00000 + 6.92820i) q^{67} +4.00000 q^{68} +(1.00000 + 5.19615i) q^{70} +(4.00000 + 6.92820i) q^{71} +(-4.50000 + 7.79423i) q^{73} -7.00000 q^{74} +(-2.50000 + 4.33013i) q^{76} +(1.00000 + 5.19615i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-5.00000 + 8.66025i) q^{82} +14.0000 q^{83} +(4.00000 + 6.92820i) q^{85} +(3.50000 + 6.06218i) q^{86} +(1.00000 + 1.73205i) q^{88} -6.00000 q^{89} +(8.00000 + 5.19615i) q^{91} +2.00000 q^{92} +(-6.00000 - 10.3923i) q^{94} -10.0000 q^{95} +(-8.50000 - 14.7224i) q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8} - 2 q^{10} - 2 q^{11} - 7 q^{13} + 5 q^{14} + 2 q^{16} + 8 q^{17} - 5 q^{19} + 2 q^{20} + 2 q^{22} + 4 q^{23} + q^{25} + 7 q^{26} - 5 q^{28} + 8 q^{29} - 2 q^{32} - 8 q^{34} - 2 q^{35} + 14 q^{37} + 5 q^{38} - 2 q^{40} + 10 q^{41} - 7 q^{43} - 2 q^{44} - 4 q^{46} + 12 q^{47} + 11 q^{49} - q^{50} - 7 q^{52} + 6 q^{53} + 4 q^{55} + 5 q^{56} - 8 q^{58} + q^{61} + 2 q^{64} - 4 q^{65} + 8 q^{67} + 8 q^{68} + 2 q^{70} + 8 q^{71} - 9 q^{73} - 14 q^{74} - 5 q^{76} + 2 q^{77} - 8 q^{79} + 2 q^{80} - 10 q^{82} + 28 q^{83} + 8 q^{85} + 7 q^{86} + 2 q^{88} - 12 q^{89} + 16 q^{91} + 4 q^{92} - 12 q^{94} - 20 q^{95} - 17 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8 - 2 * q^10 - 2 * q^11 - 7 * q^13 + 5 * q^14 + 2 * q^16 + 8 * q^17 - 5 * q^19 + 2 * q^20 + 2 * q^22 + 4 * q^23 + q^25 + 7 * q^26 - 5 * q^28 + 8 * q^29 - 2 * q^32 - 8 * q^34 - 2 * q^35 + 14 * q^37 + 5 * q^38 - 2 * q^40 + 10 * q^41 - 7 * q^43 - 2 * q^44 - 4 * q^46 + 12 * q^47 + 11 * q^49 - q^50 - 7 * q^52 + 6 * q^53 + 4 * q^55 + 5 * q^56 - 8 * q^58 + q^61 + 2 * q^64 - 4 * q^65 + 8 * q^67 + 8 * q^68 + 2 * q^70 + 8 * q^71 - 9 * q^73 - 14 * q^74 - 5 * q^76 + 2 * q^77 - 8 * q^79 + 2 * q^80 - 10 * q^82 + 28 * q^83 + 8 * q^85 + 7 * q^86 + 2 * q^88 - 12 * q^89 + 16 * q^91 + 4 * q^92 - 12 * q^94 - 20 * q^95 - 17 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$	2.50000	+	0.866025i	0.668153	+	0.231455i
$15$		0			0
$16$	1.00000			0.250000
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$		0			0
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	−0.208443	−	0.978035i	$-0.566840\pi$
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	0.951224	−	0.308500i	$-0.0998271\pi$
$30$		0			0
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−4.00000			−0.685994
$35$	−1.00000	−	5.19615i	−0.169031	−	0.878310i
$36$		0			0
$37$	7.00000			1.15079			0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000			1.15079			0.575396	+	0.817875i	$0.304848\pi$
$38$	2.50000	−	4.33013i	0.405554	−	0.702439i
$39$		0			0
$40$	−1.00000	−	1.73205i	−0.158114	−	0.273861i
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	−0.150567	−	0.988600i	$-0.548110\pi$
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	0.931436	−	0.363905i	$-0.118557\pi$
$42$		0			0
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	−0.999223	−	0.0394140i	$-0.987451\pi$
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	0.465478	−	0.885059i	$-0.345882\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$	−2.00000			−0.294884
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.856560	+	0.516047i	$0.172597\pi$
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.0186297	+	0.999826i	$0.494070\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$	2.00000	−	3.46410i	0.269680	−	0.467099i
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$		0			0
$58$	−4.00000	+	6.92820i	−0.525226	+	0.909718i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	−	6.92820i	−0.248069	−	0.859338i
$66$		0			0
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	0.999915	−	0.0130248i	$-0.00414604\pi$
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	−0.511237	+	0.859440i	$0.670813\pi$
$68$	4.00000			0.485071
$69$		0			0
$70$	1.00000	+	5.19615i	0.119523	+	0.621059i
$71$	4.00000	+	6.92820i	0.474713	+	0.822226i	0.999581	−	0.0289572i	$-0.00921865\pi$
$71$	4.00000	+	6.92820i	0.474713	+	0.822226i	−0.524868	+	0.851184i	$0.675885\pi$
$72$		0			0
$73$	−4.50000	+	7.79423i	−0.526685	+	0.912245i	0.472831	+	0.881153i	$0.343232\pi$
$73$	−4.50000	+	7.79423i	−0.526685	+	0.912245i	−0.999517	+	0.0310925i	$0.990101\pi$
$74$	−7.00000			−0.813733
$75$		0			0
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$	1.00000	+	5.19615i	0.113961	+	0.592157i
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$		0			0
$82$	−5.00000	+	8.66025i	−0.552158	+	0.956365i
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$		0			0
$85$	4.00000	+	6.92820i	0.433861	+	0.751469i
$86$	3.50000	+	6.06218i	0.377415	+	0.653701i
$87$		0			0
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	8.00000	+	5.19615i	0.838628	+	0.544705i
$92$	2.00000			0.208514
$93$		0			0
$94$	−6.00000	−	10.3923i	−0.618853	−	1.07188i
$95$	−10.0000			−1.02598
$96$		0			0
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	−0.868976	−	0.494854i	$-0.835222\pi$
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	0.00593185	−	0.999982i	$-0.498112\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	9.50000	−	16.4545i	0.909935	−	1.57605i	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	9.50000	−	16.4545i	0.909935	−	1.57605i	0.814152	−	0.580651i	$-0.197202\pi$
$110$	−2.00000	+	3.46410i	−0.190693	+	0.330289i
$111$		0			0
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	4.00000	+	6.92820i	0.376288	+	0.651751i	0.990519	−	0.137376i	$-0.0438669\pi$
$113$	4.00000	+	6.92820i	0.376288	+	0.651751i	−0.614231	+	0.789127i	$0.710534\pi$
$114$		0			0
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	4.00000	−	6.92820i	0.371391	−	0.643268i
$117$		0			0
$118$		0			0
$119$	−10.0000	−	3.46410i	−0.916698	−	0.317554i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−0.500000	+	0.866025i	−0.0452679	+	0.0784063i
$123$		0			0
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	−9.50000	+	16.4545i	−0.842989	+	1.46010i	0.0443678	+	0.999015i	$0.485873\pi$
$127$	−9.50000	+	16.4545i	−0.842989	+	1.46010i	−0.887357	+	0.461084i	$0.847461\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	2.00000	+	6.92820i	0.175412	+	0.607644i
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	10.0000	−	8.66025i	0.867110	−	0.750939i
$134$	−4.00000	−	6.92820i	−0.345547	−	0.598506i
$135$		0			0
$136$	−4.00000			−0.342997
$137$	−2.00000			−0.170872			−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000			−0.170872			−0.0854358	+	0.996344i	$0.527228\pi$
$138$		0			0
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$	−1.00000	−	5.19615i	−0.0845154	−	0.439155i
$141$		0			0
$142$	−4.00000	−	6.92820i	−0.335673	−	0.581402i
$143$	2.00000	+	6.92820i	0.167248	+	0.579365i
$144$		0			0
$145$	16.0000			1.32873
$146$	4.50000	−	7.79423i	0.372423	−	0.645055i
$147$		0			0
$148$	7.00000			0.575396
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$		0			0
$154$	−1.00000	−	5.19615i	−0.0805823	−	0.418718i
$155$		0			0
$156$		0			0
$157$	8.50000	−	14.7224i	0.678374	−	1.17498i	−0.297097	−	0.954847i	$-0.596018\pi$
$157$	8.50000	−	14.7224i	0.678374	−	1.17498i	0.975470	−	0.220131i	$-0.0706483\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$		0			0
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	−5.00000	−	1.73205i	−0.394055	−	0.136505i
$162$		0			0
$163$	1.50000	−	2.59808i	0.117489	−	0.203497i	−0.801283	−	0.598286i	$-0.795849\pi$
$163$	1.50000	−	2.59808i	0.117489	−	0.203497i	0.918772	+	0.394789i	$0.129182\pi$
$164$	5.00000	−	8.66025i	0.390434	−	0.676252i
$165$		0			0
$166$	−14.0000			−1.08661
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	−4.00000	−	6.92820i	−0.306786	−	0.531369i
$171$		0			0
$172$	−3.50000	−	6.06218i	−0.266872	−	0.462237i
$173$	−1.00000	+	1.73205i	−0.0760286	+	0.131685i	−0.901533	−	0.432710i	$-0.857557\pi$
$173$	−1.00000	+	1.73205i	−0.0760286	+	0.131685i	0.825505	+	0.564396i	$0.190891\pi$
$174$		0			0
$175$	−2.00000	+	1.73205i	−0.151186	+	0.130931i
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		0			0
$178$	6.00000			0.449719
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	−8.00000	−	5.19615i	−0.592999	−	0.385164i
$183$		0			0
$184$	−2.00000			−0.147442
$185$	7.00000	+	12.1244i	0.514650	+	0.891400i
$186$		0			0
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$	6.00000	+	10.3923i	0.437595	+	0.757937i
$189$		0			0
$190$	10.0000			0.725476
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.00454614	−	0.999990i	$-0.498553\pi$
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.863743	−	0.503932i	$-0.168114\pi$
$192$		0			0
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$	8.50000	+	14.7224i	0.610264	+	1.05701i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	6.00000	−	10.3923i	0.427482	−	0.740421i	−0.569166	−	0.822222i	$-0.692734\pi$
$197$	6.00000	−	10.3923i	0.427482	−	0.740421i	0.996649	+	0.0818013i	$0.0260673\pi$
$198$		0			0
$199$	7.00000			0.496217			0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000			0.496217			0.248108	+	0.968732i	$0.420191\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	3.00000	+	5.19615i	0.211079	+	0.365600i
$203$	−16.0000	+	13.8564i	−1.12298	+	0.972529i
$204$		0			0
$205$	20.0000			1.39686
$206$	−2.50000	−	4.33013i	−0.174183	−	0.301694i
$207$		0			0
$208$	−3.50000	−	0.866025i	−0.242681	−	0.0600481i
$209$	10.0000			0.691714
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$	−12.0000			−0.820303
$215$	7.00000	−	12.1244i	0.477396	−	0.826874i
$216$		0			0
$217$		0			0
$218$	−9.50000	+	16.4545i	−0.643421	+	1.11444i
$219$		0			0
$220$	2.00000	−	3.46410i	0.134840	−	0.233550i
$221$	−14.0000	−	3.46410i	−0.941742	−	0.233021i
$222$		0			0
$223$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$223$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$	−4.00000	−	6.92820i	−0.266076	−	0.460857i
$227$	−2.00000			−0.132745			−0.0663723	−	0.997795i	$-0.521143\pi$
$227$	−2.00000			−0.132745			−0.0663723	+	0.997795i	$0.521143\pi$
$228$		0			0
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$	−2.00000	−	3.46410i	−0.131876	−	0.228416i
$231$		0			0
$232$	−4.00000	+	6.92820i	−0.262613	+	0.454859i
$233$	−10.0000	−	17.3205i	−0.655122	−	1.13470i	−0.981863	−	0.189590i	$-0.939284\pi$
$233$	−10.0000	−	17.3205i	−0.655122	−	1.13470i	0.326741	−	0.945114i	$-0.394049\pi$
$234$		0			0
$235$	−12.0000	+	20.7846i	−0.782794	+	1.35584i
$236$		0			0
$237$		0			0
$238$	10.0000	+	3.46410i	0.648204	+	0.224544i
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$		0			0
$241$	−22.0000			−1.41714			−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000			−1.41714			−0.708572	+	0.705638i	$0.750660\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$	−2.00000	+	13.8564i	−0.127775	+	0.885253i
$246$		0			0
$247$	12.5000	−	12.9904i	0.795356	−	0.826558i
$248$		0			0
$249$		0			0
$250$	−12.0000			−0.758947
$251$	−4.00000	−	6.92820i	−0.252478	−	0.437304i	0.711730	−	0.702454i	$-0.247912\pi$
$251$	−4.00000	−	6.92820i	−0.252478	−	0.437304i	−0.964207	+	0.265149i	$0.914579\pi$
$252$		0			0
$253$	−2.00000	−	3.46410i	−0.125739	−	0.217786i
$254$	9.50000	−	16.4545i	0.596083	−	1.03245i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$		0			0
$259$	−17.5000	−	6.06218i	−1.08740	−	0.376685i
$260$	−2.00000	−	6.92820i	−0.124035	−	0.429669i
$261$		0			0
$262$	3.00000	+	5.19615i	0.185341	+	0.321019i
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	0.797752	−	0.602986i	$-0.206023\pi$
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	−0.921077	+	0.389380i	$0.872689\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$	−10.0000	+	8.66025i	−0.613139	+	0.530994i
$267$		0			0
$268$	4.00000	+	6.92820i	0.244339	+	0.423207i
$269$	−12.0000			−0.731653			−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000			−0.731653			−0.365826	+	0.930683i	$0.619214\pi$
$270$		0			0
$271$	3.00000			0.182237			0.0911185	−	0.995840i	$-0.470956\pi$
$271$	3.00000			0.182237			0.0911185	+	0.995840i	$0.470956\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	2.00000			0.120824
$275$	−2.00000			−0.120605
$276$		0			0
$277$	13.0000			0.781094			0.390547	−	0.920583i	$-0.372286\pi$
$277$	13.0000			0.781094			0.390547	+	0.920583i	$0.372286\pi$
$278$	2.00000	+	3.46410i	0.119952	+	0.207763i
$279$		0			0
$280$	1.00000	+	5.19615i	0.0597614	+	0.310530i
$281$	−8.00000			−0.477240			−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000			−0.477240			−0.238620	+	0.971113i	$0.576695\pi$
$282$		0			0
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	0.991960	−	0.126550i	$-0.0403903\pi$
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	−0.605575	+	0.795788i	$0.707057\pi$
$284$	4.00000	+	6.92820i	0.237356	+	0.411113i
$285$		0			0
$286$	−2.00000	−	6.92820i	−0.118262	−	0.409673i
$287$	−20.0000	+	17.3205i	−1.18056	+	1.02240i
$288$		0			0
$289$	−1.00000			−0.0588235
$290$	−16.0000			−0.939552
$291$		0			0
$292$	−4.50000	+	7.79423i	−0.263343	+	0.456123i
$293$	14.0000	+	24.2487i	0.817889	+	1.41662i	0.907235	+	0.420624i	$0.138189\pi$
$293$	14.0000	+	24.2487i	0.817889	+	1.41662i	−0.0893462	+	0.996001i	$0.528478\pi$
$294$		0			0
$295$		0			0
$296$	−7.00000			−0.406867
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−7.00000	−	1.73205i	−0.404820	−	0.100167i
$300$		0			0
$301$	3.50000	+	18.1865i	0.201737	+	1.04825i
$302$	−8.00000	+	13.8564i	−0.460348	+	0.797347i
$303$		0			0
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$	2.00000			0.114520
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	1.00000	+	5.19615i	0.0569803	+	0.296078i
$309$		0			0
$310$		0			0
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	−0.0301210	−	0.999546i	$-0.509589\pi$
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	0.880693	−	0.473688i	$-0.157077\pi$
$312$		0			0
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	0.993757	+	0.111563i	$0.0355857\pi$
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	−0.400262	+	0.916401i	$0.631081\pi$
$314$	−8.50000	+	14.7224i	−0.479683	+	0.830835i
$315$		0			0
$316$	−4.00000	−	6.92820i	−0.225018	−	0.389742i
$317$	−1.00000	−	1.73205i	−0.0561656	−	0.0972817i	0.836576	−	0.547852i	$-0.184554\pi$
$317$	−1.00000	−	1.73205i	−0.0561656	−	0.0972817i	−0.892741	+	0.450570i	$0.851221\pi$
$318$		0			0
$319$	−16.0000			−0.895828
$320$	1.00000	+	1.73205i	0.0559017	+	0.0968246i
$321$		0			0
$322$	5.00000	+	1.73205i	0.278639	+	0.0965234i
$323$	−10.0000	+	17.3205i	−0.556415	+	0.963739i
$324$		0			0
$325$	−2.50000	+	2.59808i	−0.138675	+	0.144115i
$326$	−1.50000	+	2.59808i	−0.0830773	+	0.143894i
$327$		0			0
$328$	−5.00000	+	8.66025i	−0.276079	+	0.478183i
$329$	−6.00000	−	31.1769i	−0.330791	−	1.71884i
$330$		0			0
$331$	7.50000	−	12.9904i	0.412237	−	0.714016i	−0.582897	−	0.812546i	$-0.698081\pi$
$331$	7.50000	−	12.9904i	0.412237	−	0.714016i	0.995134	+	0.0985303i	$0.0314141\pi$
$332$	14.0000			0.768350
$333$		0			0
$334$	9.00000	−	15.5885i	0.492458	−	0.852962i
$335$	−8.00000	+	13.8564i	−0.437087	+	0.757056i
$336$		0			0
$337$	−3.00000			−0.163420			−0.0817102	−	0.996656i	$-0.526038\pi$
$337$	−3.00000			−0.163420			−0.0817102	+	0.996656i	$0.526038\pi$
$338$	−11.5000	−	6.06218i	−0.625518	−	0.329739i
$339$		0			0
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$		0			0
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	3.50000	+	6.06218i	0.188707	+	0.326851i
$345$		0			0
$346$	1.00000	−	1.73205i	0.0537603	−	0.0931156i
$347$	−8.00000			−0.429463			−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000			−0.429463			−0.214731	+	0.976673i	$0.568888\pi$
$348$		0			0
$349$	0.500000	−	0.866025i	0.0267644	−	0.0463573i	−0.852333	−	0.523000i	$-0.824813\pi$
$349$	0.500000	−	0.866025i	0.0267644	−	0.0463573i	0.879097	+	0.476642i	$0.158146\pi$
$350$	2.00000	−	1.73205i	0.106904	−	0.0925820i
$351$		0			0
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	7.00000	+	12.1244i	0.372572	+	0.645314i	0.989960	−	0.141344i	$-0.0451425\pi$
$353$	7.00000	+	12.1244i	0.372572	+	0.645314i	−0.617388	+	0.786659i	$0.711809\pi$
$354$		0			0
$355$	−8.00000	+	13.8564i	−0.424596	+	0.735422i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−3.00000	−	5.19615i	−0.158555	−	0.274625i
$359$	−18.0000	−	31.1769i	−0.950004	−	1.64545i	−0.745409	−	0.666608i	$-0.767746\pi$
$359$	−18.0000	−	31.1769i	−0.950004	−	1.64545i	−0.204595	−	0.978847i	$-0.565588\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−13.0000			−0.683265
$363$		0			0
$364$	8.00000	+	5.19615i	0.419314	+	0.272352i
$365$	−18.0000			−0.942163
$366$		0			0
$367$	−16.5000	−	28.5788i	−0.861293	−	1.49180i	−0.870681	−	0.491847i	$-0.836322\pi$
$367$	−16.5000	−	28.5788i	−0.861293	−	1.49180i	0.00938849	−	0.999956i	$-0.497012\pi$
$368$	2.00000			0.104257
$369$		0			0
$370$	−7.00000	−	12.1244i	−0.363913	−	0.630315i
$371$	−12.0000	+	10.3923i	−0.623009	+	0.539542i
$372$		0			0
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.0291379	+	0.999575i	$0.509276\pi$
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.851089	+	0.525022i	$0.824057\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$		0			0
$376$	−6.00000	−	10.3923i	−0.309426	−	0.535942i
$377$	−20.0000	+	20.7846i	−1.03005	+	1.07046i
$378$		0			0
$379$	−14.0000	+	24.2487i	−0.719132	+	1.24557i	0.242213	+	0.970223i	$0.422127\pi$
$379$	−14.0000	+	24.2487i	−0.719132	+	1.24557i	−0.961344	+	0.275349i	$0.911206\pi$
$380$	−10.0000			−0.512989
$381$		0			0
$382$	−12.0000	+	20.7846i	−0.613973	+	1.06343i
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.119974	+	0.992777i	$0.538281\pi$
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.799783	+	0.600289i	$0.795052\pi$
$384$		0			0
$385$	−8.00000	+	6.92820i	−0.407718	+	0.353094i
$386$	5.50000	+	9.52628i	0.279943	+	0.484875i
$387$		0			0
$388$	−8.50000	−	14.7224i	−0.431522	−	0.747418i
$389$	−19.0000	+	32.9090i	−0.963338	+	1.66855i	−0.249323	+	0.968420i	$0.580208\pi$
$389$	−19.0000	+	32.9090i	−0.963338	+	1.66855i	−0.714015	+	0.700130i	$0.753125\pi$
$390$		0			0
$391$	8.00000			0.404577
$392$	−5.50000	−	4.33013i	−0.277792	−	0.218704i
$393$		0			0
$394$	−6.00000	+	10.3923i	−0.302276	+	0.523557i
$395$	8.00000	−	13.8564i	0.402524	−	0.697191i
$396$		0			0
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	−0.360723	−	0.932673i	$-0.617470\pi$
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	0.988080	−	0.153941i	$-0.0491966\pi$
$398$	−7.00000			−0.350878
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−10.0000			−0.499376			−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000			−0.499376			−0.249688	+	0.968326i	$0.580328\pi$
$402$		0			0
$403$		0			0
$404$	−3.00000	−	5.19615i	−0.149256	−	0.258518i
$405$		0			0
$406$	16.0000	−	13.8564i	0.794067	−	0.687682i
$407$	−7.00000	−	12.1244i	−0.346977	−	0.600982i
$408$		0			0
$409$	−19.0000			−0.939490			−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000			−0.939490			−0.469745	+	0.882802i	$0.655654\pi$
$410$	−20.0000			−0.987730
$411$		0			0
$412$	2.50000	+	4.33013i	0.123166	+	0.213330i
$413$		0			0
$414$		0			0
$415$	14.0000	+	24.2487i	0.687233	+	1.19032i
$416$	3.50000	+	0.866025i	0.171602	+	0.0424604i
$417$		0			0
$418$	−10.0000			−0.489116
$419$	5.00000	−	8.66025i	0.244266	−	0.423081i	−0.717659	−	0.696395i	$-0.754786\pi$
$419$	5.00000	−	8.66025i	0.244266	−	0.423081i	0.961925	+	0.273314i	$0.0881197\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	6.50000	−	11.2583i	0.316415	−	0.548047i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$	−2.00000	+	1.73205i	−0.0967868	+	0.0838198i
$428$	12.0000			0.580042
$429$		0			0
$430$	−7.00000	+	12.1244i	−0.337570	+	0.584688i
$431$	−7.00000	−	12.1244i	−0.337178	−	0.584010i	0.646723	−	0.762725i	$-0.276139\pi$
$431$	−7.00000	−	12.1244i	−0.337178	−	0.584010i	−0.983901	+	0.178716i	$0.942806\pi$
$432$		0			0
$433$	9.00000	+	15.5885i	0.432512	+	0.749133i	0.997089	−	0.0762473i	$-0.0242938\pi$
$433$	9.00000	+	15.5885i	0.432512	+	0.749133i	−0.564577	+	0.825381i	$0.690961\pi$
$434$		0			0
$435$		0			0
$436$	9.50000	−	16.4545i	0.454967	−	0.788027i
$437$	−5.00000	+	8.66025i	−0.239182	+	0.414276i
$438$		0			0
$439$	25.0000			1.19318			0.596592	−	0.802544i	$-0.296521\pi$
$439$	25.0000			1.19318			0.596592	+	0.802544i	$0.296521\pi$
$440$	−2.00000	+	3.46410i	−0.0953463	+	0.165145i
$441$		0			0
$442$	14.0000	+	3.46410i	0.665912	+	0.164771i
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	0.785916	−	0.618333i	$-0.212192\pi$
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	−0.928450	+	0.371457i	$0.878858\pi$
$444$		0			0
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$		0			0
$447$		0			0
$448$	−2.50000	−	0.866025i	−0.118114	−	0.0409159i
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	0.571660	−	0.820491i	$-0.306300\pi$
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	−0.996396	+	0.0848262i	$0.972967\pi$
$450$		0			0
$451$	−20.0000			−0.941763
$452$	4.00000	+	6.92820i	0.188144	+	0.325875i
$453$		0			0
$454$	2.00000			0.0938647
$455$	−1.00000	+	19.0526i	−0.0468807	+	0.893198i
$456$		0			0
$457$	6.00000			0.280668			0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000			0.280668			0.140334	+	0.990104i	$0.455182\pi$
$458$	0.500000	+	0.866025i	0.0233635	+	0.0404667i
$459$		0			0
$460$	2.00000	+	3.46410i	0.0932505	+	0.161515i
$461$	16.0000	+	27.7128i	0.745194	+	1.29071i	0.950104	+	0.311933i	$0.100977\pi$
$461$	16.0000	+	27.7128i	0.745194	+	1.29071i	−0.204910	+	0.978781i	$0.565690\pi$
$462$		0			0
$463$	−27.0000			−1.25480			−0.627398	−	0.778699i	$-0.715880\pi$
$463$	−27.0000			−1.25480			−0.627398	+	0.778699i	$0.715880\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$		0			0
$466$	10.0000	+	17.3205i	0.463241	+	0.802357i
$467$	1.00000	+	1.73205i	0.0462745	+	0.0801498i	0.888235	−	0.459390i	$-0.151932\pi$
$467$	1.00000	+	1.73205i	0.0462745	+	0.0801498i	−0.841960	+	0.539539i	$0.818598\pi$
$468$		0			0
$469$	−4.00000	−	20.7846i	−0.184703	−	0.959744i
$470$	12.0000	−	20.7846i	0.553519	−	0.958723i
$471$		0			0
$472$		0			0
$473$	−7.00000	+	12.1244i	−0.321860	+	0.557478i
$474$		0			0
$475$	2.50000	+	4.33013i	0.114708	+	0.198680i
$476$	−10.0000	−	3.46410i	−0.458349	−	0.158777i
$477$		0			0
$478$	−18.0000			−0.823301
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	−24.5000	−	6.06218i	−1.11710	−	0.276412i
$482$	22.0000			1.00207
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	17.0000	−	29.4449i	0.771930	−	1.33702i
$486$		0			0
$487$	−25.0000			−1.13286			−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−25.0000			−1.13286			−0.566429	+	0.824110i	$0.691675\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$		0			0
$490$	2.00000	−	13.8564i	0.0903508	−	0.625969i
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	−0.761539	−	0.648119i	$-0.775556\pi$
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	0.942057	+	0.335453i	$0.108889\pi$
$492$		0			0
$493$	16.0000	−	27.7128i	0.720604	−	1.24812i
$494$	−12.5000	+	12.9904i	−0.562402	+	0.584465i
$495$		0			0
$496$		0			0
$497$	−4.00000	−	20.7846i	−0.179425	−	0.932317i
$498$		0			0
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	−0.997532	−	0.0702185i	$-0.977630\pi$
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	0.437955	−	0.898997i	$-0.355703\pi$
$500$	12.0000			0.536656
$501$		0			0
$502$	4.00000	+	6.92820i	0.178529	+	0.309221i
$503$	−7.00000	−	12.1244i	−0.312115	−	0.540598i	0.666705	−	0.745321i	$-0.267704\pi$
$503$	−7.00000	−	12.1244i	−0.312115	−	0.540598i	−0.978820	+	0.204723i	$0.934371\pi$
$504$		0			0
$505$	6.00000	−	10.3923i	0.266996	−	0.462451i
$506$	2.00000	+	3.46410i	0.0889108	+	0.153998i
$507$		0			0
$508$	−9.50000	+	16.4545i	−0.421494	+	0.730050i
$509$	6.00000			0.265945			0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000			0.265945			0.132973	+	0.991120i	$0.457548\pi$
$510$		0			0
$511$	18.0000	−	15.5885i	0.796273	−	0.689593i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	6.00000			0.264649
$515$	−5.00000	+	8.66025i	−0.220326	+	0.381616i
$516$		0			0
$517$	12.0000	−	20.7846i	0.527759	−	0.914106i
$518$	17.5000	+	6.06218i	0.768906	+	0.266357i
$519$		0			0
$520$	2.00000	+	6.92820i	0.0877058	+	0.303822i
$521$	18.0000	−	31.1769i	0.788594	−	1.36589i	−0.138234	−	0.990400i	$-0.544143\pi$
$521$	18.0000	−	31.1769i	0.788594	−	1.36589i	0.926828	−	0.375486i	$-0.122524\pi$
$522$		0			0
$523$	−9.00000			−0.393543			−0.196771	−	0.980449i	$-0.563046\pi$
$523$	−9.00000			−0.393543			−0.196771	+	0.980449i	$0.563046\pi$
$524$	−3.00000	−	5.19615i	−0.131056	−	0.226995i
$525$		0			0
$526$	2.00000	+	3.46410i	0.0872041	+	0.151042i
$527$		0			0
$528$		0			0
$529$	−19.0000			−0.826087
$530$	−12.0000			−0.521247
$531$		0			0
$532$	10.0000	−	8.66025i	0.433555	−	0.375470i
$533$	−25.0000	+	25.9808i	−1.08287	+	1.12535i
$534$		0			0
$535$	12.0000	+	20.7846i	0.518805	+	0.898597i
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$		0			0
$538$	12.0000			0.517357
$539$	2.00000	−	13.8564i	0.0861461	−	0.596838i
$540$		0			0
$541$	5.50000	+	9.52628i	0.236463	+	0.409567i	0.959697	−	0.281037i	$-0.0906783\pi$
$541$	5.50000	+	9.52628i	0.236463	+	0.409567i	−0.723234	+	0.690604i	$0.757345\pi$
$542$	−3.00000			−0.128861
$543$		0			0
$544$	−4.00000			−0.171499
$545$	38.0000			1.62774
$546$		0			0
$547$	−25.0000			−1.06892			−0.534461	−	0.845193i	$-0.679486\pi$
$547$	−25.0000			−1.06892			−0.534461	+	0.845193i	$0.679486\pi$
$548$	−2.00000			−0.0854358
$549$		0			0
$550$	2.00000			0.0852803
$551$	20.0000	+	34.6410i	0.852029	+	1.47576i
$552$		0			0
$553$	4.00000	+	20.7846i	0.170097	+	0.883852i
$554$	−13.0000			−0.552317
$555$		0			0
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	19.0000	+	32.9090i	0.805056	+	1.39440i	0.916253	+	0.400599i	$0.131198\pi$
$557$	19.0000	+	32.9090i	0.805056	+	1.39440i	−0.111198	+	0.993798i	$0.535469\pi$
$558$		0			0
$559$	7.00000	+	24.2487i	0.296068	+	1.02561i
$560$	−1.00000	−	5.19615i	−0.0422577	−	0.219578i
$561$		0			0
$562$	8.00000			0.337460
$563$	26.0000			1.09577			0.547885	−	0.836554i	$-0.315433\pi$
$563$	26.0000			1.09577			0.547885	+	0.836554i	$0.315433\pi$
$564$		0			0
$565$	−8.00000	+	13.8564i	−0.336563	+	0.582943i
$566$	−6.50000	−	11.2583i	−0.273215	−	0.473223i
$567$		0			0
$568$	−4.00000	−	6.92820i	−0.167836	−	0.290701i
$569$	20.0000			0.838444			0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000			0.838444			0.419222	+	0.907884i	$0.362303\pi$
$570$		0			0
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$	2.00000	+	6.92820i	0.0836242	+	0.289683i
$573$		0			0
$574$	20.0000	−	17.3205i	0.834784	−	0.722944i
$575$	1.00000	−	1.73205i	0.0417029	−	0.0722315i
$576$		0			0
$577$	−13.5000	+	23.3827i	−0.562012	+	0.973434i	0.435308	+	0.900281i	$0.356639\pi$
$577$	−13.5000	+	23.3827i	−0.562012	+	0.973434i	−0.997321	+	0.0731526i	$0.976694\pi$
$578$	1.00000			0.0415945
$579$		0			0
$580$	16.0000			0.664364
$581$	−35.0000	−	12.1244i	−1.45204	−	0.503003i
$582$		0			0
$583$	−12.0000			−0.496989
$584$	4.50000	−	7.79423i	0.186211	−	0.322527i
$585$		0			0
$586$	−14.0000	−	24.2487i	−0.578335	−	1.00171i
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	−0.618322	−	0.785925i	$-0.712187\pi$
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	0.989792	+	0.142520i	$0.0455206\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	7.00000			0.287698
$593$	−16.0000	−	27.7128i	−0.657041	−	1.13803i	−0.981378	−	0.192087i	$-0.938474\pi$
$593$	−16.0000	−	27.7128i	−0.657041	−	1.13803i	0.324337	−	0.945942i	$-0.394859\pi$
$594$		0			0
$595$	−4.00000	−	20.7846i	−0.163984	−	0.852086i
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		0			0
$598$	7.00000	+	1.73205i	0.286251	+	0.0708288i
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$	−3.50000	−	18.1865i	−0.142649	−	0.741228i
$603$		0			0
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$	14.0000			0.569181
$606$		0			0
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	−0.999279	−	0.0379540i	$-0.987916\pi$
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	0.532509	+	0.846424i	$0.321249\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	−2.00000			−0.0809776
$611$	−12.0000	−	41.5692i	−0.485468	−	1.68171i
$612$		0			0
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$	12.0000			0.484281
$615$		0			0
$616$	−1.00000	−	5.19615i	−0.0402911	−	0.209359i
$617$	10.0000	+	17.3205i	0.402585	+	0.697297i	0.994037	−	0.109043i	$-0.0347785\pi$
$617$	10.0000	+	17.3205i	0.402585	+	0.697297i	−0.591452	+	0.806340i	$0.701445\pi$
$618$		0			0
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	−0.787075	−	0.616858i	$-0.788405\pi$
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	0.927752	+	0.373198i	$0.121739\pi$
$620$		0			0
$621$		0			0
$622$	−15.0000	+	25.9808i	−0.601445	+	1.04173i
$623$	15.0000	+	5.19615i	0.600962	+	0.208179i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−10.5000	−	18.1865i	−0.419664	−	0.726880i
$627$		0			0
$628$	8.50000	−	14.7224i	0.339187	−	0.587489i
$629$	28.0000			1.11643
$630$		0			0
$631$	−12.5000	−	21.6506i	−0.497617	−	0.861898i	0.502379	−	0.864647i	$-0.332458\pi$
$631$	−12.5000	−	21.6506i	−0.497617	−	0.861898i	−0.999996	+	0.00274930i	$0.999125\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$		0			0
$634$	1.00000	+	1.73205i	0.0397151	+	0.0687885i
$635$	−38.0000			−1.50798
$636$		0			0
$637$	−15.5000	−	19.9186i	−0.614132	−	0.789203i
$638$	16.0000			0.633446
$639$		0			0
$640$	−1.00000	−	1.73205i	−0.0395285	−	0.0684653i
$641$	−34.0000			−1.34292			−0.671460	−	0.741041i	$-0.734332\pi$
$641$	−34.0000			−1.34292			−0.671460	+	0.741041i	$0.734332\pi$
$642$		0			0
$643$	6.50000	+	11.2583i	0.256335	+	0.443985i	0.965257	−	0.261301i	$-0.0841516\pi$
$643$	6.50000	+	11.2583i	0.256335	+	0.443985i	−0.708922	+	0.705287i	$0.750818\pi$
$644$	−5.00000	−	1.73205i	−0.197028	−	0.0682524i
$645$		0			0
$646$	10.0000	−	17.3205i	0.393445	−	0.681466i
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$		0			0
$649$		0			0
$650$	2.50000	−	2.59808i	0.0980581	−	0.101905i
$651$		0			0
$652$	1.50000	−	2.59808i	0.0587445	−	0.101749i
$653$	−36.0000			−1.40879			−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000			−1.40879			−0.704394	+	0.709809i	$0.748781\pi$
$654$		0			0
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$	5.00000	−	8.66025i	0.195217	−	0.338126i
$657$		0			0
$658$	6.00000	+	31.1769i	0.233904	+	1.21540i
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	0.952940	+	0.303160i	$0.0980418\pi$
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	−0.213925	+	0.976850i	$0.568625\pi$
$662$	−7.50000	+	12.9904i	−0.291496	+	0.504885i
$663$		0			0
$664$	−14.0000			−0.543305
$665$	25.0000	+	8.66025i	0.969458	+	0.335830i
$666$		0			0
$667$	8.00000	−	13.8564i	0.309761	−	0.536522i
$668$	−9.00000	+	15.5885i	−0.348220	+	0.603136i
$669$		0			0
$670$	8.00000	−	13.8564i	0.309067	−	0.535320i
$671$	−2.00000			−0.0772091
$672$		0			0
$673$	−7.50000	+	12.9904i	−0.289104	+	0.500742i	−0.973596	−	0.228278i	$-0.926691\pi$
$673$	−7.50000	+	12.9904i	−0.289104	+	0.500742i	0.684492	+	0.729020i	$0.260024\pi$
$674$	3.00000			0.115556
$675$		0			0
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	1.00000	+	1.73205i	0.0384331	+	0.0665681i	0.884602	−	0.466347i	$-0.154430\pi$
$677$	1.00000	+	1.73205i	0.0384331	+	0.0665681i	−0.846169	+	0.532915i	$0.821097\pi$
$678$		0			0
$679$	8.50000	+	44.1673i	0.326200	+	1.69499i
$680$	−4.00000	−	6.92820i	−0.153393	−	0.265684i
$681$		0			0
$682$		0			0
$683$	10.0000			0.382639			0.191320	−	0.981528i	$-0.438723\pi$
$683$	10.0000			0.382639			0.191320	+	0.981528i	$0.438723\pi$
$684$		0			0
$685$	−2.00000	−	3.46410i	−0.0764161	−	0.132357i
$686$	10.0000	+	15.5885i	0.381802	+	0.595170i
$687$		0			0
$688$	−3.50000	−	6.06218i	−0.133436	−	0.231118i
$689$	−15.0000	+	15.5885i	−0.571454	+	0.593873i
$690$		0			0
$691$	−23.0000			−0.874961			−0.437481	−	0.899228i	$-0.644129\pi$
$691$	−23.0000			−0.874961			−0.437481	+	0.899228i	$0.644129\pi$
$692$	−1.00000	+	1.73205i	−0.0380143	+	0.0658427i
$693$		0			0
$694$	8.00000			0.303676
$695$	4.00000	−	6.92820i	0.151729	−	0.262802i
$696$		0			0
$697$	20.0000	−	34.6410i	0.757554	−	1.31212i
$698$	−0.500000	+	0.866025i	−0.0189253	+	0.0327795i
$699$		0			0
$700$	−2.00000	+	1.73205i	−0.0755929	+	0.0654654i
$701$	48.0000			1.81293			0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000			1.81293			0.906467	+	0.422276i	$0.138769\pi$
$702$		0			0
$703$	−17.5000	+	30.3109i	−0.660025	+	1.14320i
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$		0			0
$706$	−7.00000	−	12.1244i	−0.263448	−	0.456306i
$707$	3.00000	+	15.5885i	0.112827	+	0.586264i
$708$		0			0
$709$	−22.5000	+	38.9711i	−0.845005	+	1.46359i	0.0406114	+	0.999175i	$0.487069\pi$
$709$	−22.5000	+	38.9711i	−0.845005	+	1.46359i	−0.885617	+	0.464417i	$0.846264\pi$
$710$	8.00000	−	13.8564i	0.300235	−	0.520022i
$711$		0			0
$712$	6.00000			0.224860
$713$		0			0
$714$		0			0
$715$	−10.0000	+	10.3923i	−0.373979	+	0.388650i
$716$	3.00000	+	5.19615i	0.112115	+	0.194189i
$717$		0			0
$718$	18.0000	+	31.1769i	0.671754	+	1.16351i
$719$	5.00000	−	8.66025i	0.186469	−	0.322973i	−0.757602	−	0.652717i	$-0.773629\pi$
$719$	5.00000	−	8.66025i	0.186469	−	0.322973i	0.944070	+	0.329744i	$0.106962\pi$
$720$		0			0
$721$	−2.50000	−	12.9904i	−0.0931049	−	0.483787i
$722$	3.00000	+	5.19615i	0.111648	+	0.193381i
$723$		0			0
$724$	13.0000			0.483141
$725$	−4.00000	−	6.92820i	−0.148556	−	0.257307i
$726$		0			0
$727$	24.0000			0.890111			0.445055	−	0.895503i	$-0.353184\pi$
$727$	24.0000			0.890111			0.445055	+	0.895503i	$0.353184\pi$
$728$	−8.00000	−	5.19615i	−0.296500	−	0.192582i
$729$		0			0
$730$	18.0000			0.666210
$731$	−14.0000	−	24.2487i	−0.517809	−	0.896871i
$732$		0			0
$733$	15.0000	+	25.9808i	0.554038	+	0.959621i	0.997978	+	0.0635649i	$0.0202470\pi$
$733$	15.0000	+	25.9808i	0.554038	+	0.959621i	−0.443940	+	0.896056i	$0.646420\pi$
$734$	16.5000	+	28.5788i	0.609026	+	1.05486i
$735$		0			0
$736$	−2.00000			−0.0737210
$737$	8.00000	−	13.8564i	0.294684	−	0.510407i
$738$		0			0
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	0.996235	−	0.0866983i	$-0.0276316\pi$
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	−0.573200	+	0.819415i	$0.694298\pi$
$740$	7.00000	+	12.1244i	0.257325	+	0.445700i
$741$		0			0
$742$	12.0000	−	10.3923i	0.440534	−	0.381514i
$743$	25.0000	−	43.3013i	0.917161	−	1.58857i	0.113455	−	0.993543i	$-0.463808\pi$
$743$	25.0000	−	43.3013i	0.917161	−	1.58857i	0.803706	−	0.595026i	$-0.202858\pi$
$744$		0			0
$745$	−12.0000			−0.439646
$746$	17.0000	−	29.4449i	0.622414	−	1.07805i
$747$		0			0
$748$	−4.00000	−	6.92820i	−0.146254	−	0.253320i
$749$	−30.0000	−	10.3923i	−1.09618	−	0.379727i
$750$		0			0
$751$	−35.0000			−1.27717			−0.638584	−	0.769552i	$-0.720480\pi$
$751$	−35.0000			−1.27717			−0.638584	+	0.769552i	$0.720480\pi$
$752$	6.00000	+	10.3923i	0.218797	+	0.378968i
$753$		0			0
$754$	20.0000	−	20.7846i	0.728357	−	0.756931i
$755$	32.0000			1.16460
$756$		0			0
$757$	1.00000	−	1.73205i	0.0363456	−	0.0629525i	−0.847280	−	0.531146i	$-0.821762\pi$
$757$	1.00000	−	1.73205i	0.0363456	−	0.0629525i	0.883626	+	0.468193i	$0.155095\pi$
$758$	14.0000	−	24.2487i	0.508503	−	0.880753i
$759$		0			0
$760$	10.0000			0.362738
$761$	−11.0000	+	19.0526i	−0.398750	+	0.690655i	−0.993572	−	0.113203i	$-0.963889\pi$
$761$	−11.0000	+	19.0526i	−0.398750	+	0.690655i	0.594822	+	0.803857i	$0.297222\pi$
$762$		0			0
$763$	−38.0000	+	32.9090i	−1.37569	+	1.19138i
$764$	12.0000	−	20.7846i	0.434145	−	0.751961i
$765$		0			0
$766$	18.0000	−	31.1769i	0.650366	−	1.12647i
$767$		0			0
$768$		0			0
$769$	20.5000	−	35.5070i	0.739249	−	1.28042i	−0.213585	−	0.976924i	$-0.568514\pi$
$769$	20.5000	−	35.5070i	0.739249	−	1.28042i	0.952834	−	0.303492i	$-0.0981526\pi$
$770$	8.00000	−	6.92820i	0.288300	−	0.249675i
$771$		0			0
$772$	−5.50000	−	9.52628i	−0.197949	−	0.342858i
$773$	−4.00000			−0.143870			−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000			−0.143870			−0.0719350	+	0.997409i	$0.522917\pi$
$774$		0			0
$775$		0			0
$776$	8.50000	+	14.7224i	0.305132	+	0.528505i
$777$		0			0
$778$	19.0000	−	32.9090i	0.681183	−	1.17984i
$779$	25.0000	+	43.3013i	0.895718	+	1.55143i
$780$		0			0
$781$	8.00000	−	13.8564i	0.286263	−	0.495821i
$782$	−8.00000			−0.286079
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	34.0000			1.21351
$786$		0			0
$787$	29.0000			1.03374			0.516869	−	0.856064i	$-0.327097\pi$
$787$	29.0000			1.03374			0.516869	+	0.856064i	$0.327097\pi$
$788$	6.00000	−	10.3923i	0.213741	−	0.370211i
$789$		0			0
$790$	−8.00000	+	13.8564i	−0.284627	+	0.492989i
$791$	−4.00000	−	20.7846i	−0.142224	−	0.739016i
$792$		0			0
$793$	−2.50000	+	2.59808i	−0.0887776	+	0.0922604i
$794$	−12.5000	+	21.6506i	−0.443608	+	0.768352i
$795$		0			0
$796$	7.00000			0.248108
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	0.661441	−	0.749997i	$-0.269945\pi$
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	−0.980237	+	0.197826i	$0.936612\pi$
$798$		0			0
$799$	24.0000	+	41.5692i	0.849059	+	1.47061i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	10.0000			0.353112
$803$	18.0000			0.635206
$804$		0			0
$805$	−2.00000	−	10.3923i	−0.0704907	−	0.366281i
$806$		0			0
$807$		0			0
$808$	3.00000	+	5.19615i	0.105540	+	0.182800i
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	0.952012	−	0.306062i	$-0.0990113\pi$
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	−0.741063	+	0.671436i	$0.765678\pi$
$810$		0			0
$811$	−49.0000			−1.72062			−0.860311	−	0.509769i	$-0.829731\pi$
$811$	−49.0000			−1.72062			−0.860311	+	0.509769i	$0.829731\pi$
$812$	−16.0000	+	13.8564i	−0.561490	+	0.486265i
$813$		0			0
$814$	7.00000	+	12.1244i	0.245350	+	0.424958i
$815$	6.00000			0.210171
$816$		0			0
$817$	35.0000			1.22449
$818$	19.0000			0.664319
$819$		0			0
$820$	20.0000			0.698430
$821$	34.0000			1.18661			0.593304	−	0.804978i	$-0.297823\pi$
$821$	34.0000			1.18661			0.593304	+	0.804978i	$0.297823\pi$
$822$		0			0
$823$	−8.00000			−0.278862			−0.139431	−	0.990232i	$-0.544527\pi$
$823$	−8.00000			−0.278862			−0.139431	+	0.990232i	$0.544527\pi$
$824$	−2.50000	−	4.33013i	−0.0870916	−	0.150847i
$825$		0			0
$826$		0			0
$827$	−8.00000			−0.278187			−0.139094	−	0.990279i	$-0.544419\pi$
$827$	−8.00000			−0.278187			−0.139094	+	0.990279i	$0.544419\pi$
$828$		0			0
$829$	1.50000	+	2.59808i	0.0520972	+	0.0902349i	0.890898	−	0.454204i	$-0.150076\pi$
$829$	1.50000	+	2.59808i	0.0520972	+	0.0902349i	−0.838801	+	0.544438i	$0.816743\pi$
$830$	−14.0000	−	24.2487i	−0.485947	−	0.841685i
$831$		0			0
$832$	−3.50000	−	0.866025i	−0.121341	−	0.0300240i
$833$	22.0000	+	17.3205i	0.762255	+	0.600120i
$834$		0			0
$835$	−36.0000			−1.24583
$836$	10.0000			0.345857
$837$		0			0
$838$	−5.00000	+	8.66025i	−0.172722	+	0.299164i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	−17.5000	−	30.3109i	−0.603448	−	1.04520i
$842$	−22.0000			−0.758170
$843$		0			0
$844$	−6.50000	+	11.2583i	−0.223739	+	0.387528i
$845$	1.00000	+	25.9808i	0.0344010	+	0.893765i
$846$		0			0
$847$	−14.0000	+	12.1244i	−0.481046	+	0.416598i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$		0			0
$850$	−2.00000	+	3.46410i	−0.0685994	+	0.118818i
$851$	14.0000			0.479914
$852$		0			0
$853$	22.0000			0.753266			0.376633	−	0.926363i	$-0.377082\pi$
$853$	22.0000			0.753266			0.376633	+	0.926363i	$0.377082\pi$
$854$	2.00000	−	1.73205i	0.0684386	−	0.0592696i
$855$		0			0
$856$	−12.0000			−0.410152
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	−0.584967	−	0.811057i	$-0.698893\pi$
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	0.994880	+	0.101068i	$0.0322260\pi$
$858$		0			0
$859$	−6.50000	−	11.2583i	−0.221777	−	0.384129i	0.733571	−	0.679613i	$-0.237852\pi$
$859$	−6.50000	−	11.2583i	−0.221777	−	0.384129i	−0.955348	+	0.295484i	$0.904519\pi$
$860$	7.00000	−	12.1244i	0.238698	−	0.413437i
$861$		0			0
$862$	7.00000	+	12.1244i	0.238421	+	0.412957i
$863$	−15.0000	−	25.9808i	−0.510606	−	0.884395i	−0.999924	−	0.0122903i	$-0.996088\pi$
$863$	−15.0000	−	25.9808i	−0.510606	−	0.884395i	0.489319	−	0.872105i	$-0.337246\pi$
$864$		0			0
$865$	−4.00000			−0.136004
$866$	−9.00000	−	15.5885i	−0.305832	−	0.529717i
$867$		0			0
$868$		0			0
$869$	−8.00000	+	13.8564i	−0.271381	+	0.470046i
$870$		0			0
$871$	−8.00000	−	27.7128i	−0.271070	−	0.939013i
$872$	−9.50000	+	16.4545i	−0.321711	+	0.557219i
$873$		0			0
$874$	5.00000	−	8.66025i	0.169128	−	0.292937i
$875$	−30.0000	−	10.3923i	−1.01419	−	0.351324i
$876$		0			0
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−25.0000			−0.843709
$879$		0			0
$880$	2.00000	−	3.46410i	0.0674200	−	0.116775i
$881$	−14.0000	+	24.2487i	−0.471672	+	0.816960i	−0.999475	−	0.0324071i	$-0.989683\pi$
$881$	−14.0000	+	24.2487i	−0.471672	+	0.816960i	0.527803	+	0.849367i	$0.323016\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	−14.0000	−	3.46410i	−0.470871	−	0.116510i
$885$		0			0
$886$	3.00000	+	5.19615i	0.100787	+	0.174568i
$887$	50.0000			1.67884			0.839418	−	0.543487i	$-0.182896\pi$
$887$	50.0000			1.67884			0.839418	+	0.543487i	$0.182896\pi$
$888$		0			0
$889$	38.0000	−	32.9090i	1.27448	−	1.10373i
$890$	6.00000	+	10.3923i	0.201120	+	0.348351i
$891$		0			0
$892$		0			0
$893$	−60.0000			−2.00782
$894$		0			0
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$	2.50000	+	0.866025i	0.0835191	+	0.0289319i
$897$		0			0
$898$	9.00000	+	15.5885i	0.300334	+	0.520194i
$899$		0			0
$900$		0			0
$901$	12.0000	−	20.7846i	0.399778	−	0.692436i
$902$	20.0000			0.665927
$903$		0			0
$904$	−4.00000	−	6.92820i	−0.133038	−	0.230429i
$905$	13.0000	+	22.5167i	0.432135	+	0.748479i
$906$		0			0
$907$	−19.5000	−	33.7750i	−0.647487	−	1.12148i	−0.983721	−	0.179702i	$-0.942487\pi$
$907$	−19.5000	−	33.7750i	−0.647487	−	1.12148i	0.336234	−	0.941778i	$-0.390847\pi$
$908$	−2.00000			−0.0663723
$909$		0			0
$910$	1.00000	−	19.0526i	0.0331497	−	0.631586i
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$	−14.0000	−	24.2487i	−0.463332	−	0.802515i
$914$	−6.00000			−0.198462
$915$		0			0
$916$	−0.500000	−	0.866025i	−0.0165205	−	0.0286143i
$917$	3.00000	+	15.5885i	0.0990687	+	0.514776i
$918$		0			0
$919$	0.500000	−	0.866025i	0.0164935	−	0.0285675i	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	0.500000	−	0.866025i	0.0164935	−	0.0285675i	0.874154	+	0.485648i	$0.161416\pi$
$920$	−2.00000	−	3.46410i	−0.0659380	−	0.114208i
$921$		0			0
$922$	−16.0000	−	27.7128i	−0.526932	−	0.912673i
$923$	−8.00000	−	27.7128i	−0.263323	−	0.912178i
$924$		0			0
$925$	3.50000	−	6.06218i	0.115079	−	0.199323i
$926$	27.0000			0.887275
$927$		0			0
$928$	−4.00000	+	6.92820i	−0.131306	+	0.227429i
$929$	24.0000	−	41.5692i	0.787414	−	1.36384i	−0.140132	−	0.990133i	$-0.544753\pi$
$929$	24.0000	−	41.5692i	0.787414	−	1.36384i	0.927546	−	0.373709i	$-0.121914\pi$
$930$		0			0
$931$	−32.5000	+	12.9904i	−1.06514	+	0.425743i
$932$	−10.0000	−	17.3205i	−0.327561	−	0.567352i
$933$		0			0
$934$	−1.00000	−	1.73205i	−0.0327210	−	0.0566744i
$935$	8.00000	−	13.8564i	0.261628	−	0.453153i
$936$		0			0
$937$	3.00000			0.0980057			0.0490029	−	0.998799i	$-0.484396\pi$
$937$	3.00000			0.0980057			0.0490029	+	0.998799i	$0.484396\pi$
$938$	4.00000	+	20.7846i	0.130605	+	0.678642i
$939$		0			0
$940$	−12.0000	+	20.7846i	−0.391397	+	0.677919i
$941$	26.0000	−	45.0333i	0.847576	−	1.46804i	−0.0357896	−	0.999359i	$-0.511395\pi$
$941$	26.0000	−	45.0333i	0.847576	−	1.46804i	0.883365	−	0.468685i	$-0.155272\pi$
$942$		0			0
$943$	10.0000	−	17.3205i	0.325645	−	0.564033i
$944$		0			0
$945$		0			0
$946$	7.00000	−	12.1244i	0.227590	−	0.394197i
$947$	−32.0000			−1.03986			−0.519930	−	0.854209i	$-0.674042\pi$
$947$	−32.0000			−1.03986			−0.519930	+	0.854209i	$0.674042\pi$
$948$		0			0
$949$	22.5000	−	23.3827i	0.730381	−	0.759034i
$950$	−2.50000	−	4.33013i	−0.0811107	−	0.140488i
$951$		0			0
$952$	10.0000	+	3.46410i	0.324102	+	0.112272i
$953$	−25.0000	−	43.3013i	−0.809829	−	1.40267i	−0.912982	−	0.408000i	$-0.866226\pi$
$953$	−25.0000	−	43.3013i	−0.809829	−	1.40267i	0.103152	−	0.994666i	$-0.467107\pi$
$954$		0			0
$955$	48.0000			1.55324
$956$	18.0000			0.582162
$957$		0			0
$958$	−12.0000	−	20.7846i	−0.387702	−	0.671520i
$959$	5.00000	+	1.73205i	0.161458	+	0.0559308i
$960$		0			0
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	24.5000	+	6.06218i	0.789912	+	0.195452i
$963$		0			0
$964$	−22.0000			−0.708572
$965$	11.0000	−	19.0526i	0.354103	−	0.613324i
$966$		0			0
$967$	−21.0000			−0.675314			−0.337657	−	0.941269i	$-0.609634\pi$
$967$	−21.0000			−0.675314			−0.337657	+	0.941269i	$0.609634\pi$
$968$	−3.50000	+	6.06218i	−0.112494	+	0.194846i
$969$		0			0
$970$	−17.0000	+	29.4449i	−0.545837	+	0.945418i
$971$	9.00000	−	15.5885i	0.288824	−	0.500257i	−0.684706	−	0.728820i	$-0.740069\pi$
$971$	9.00000	−	15.5885i	0.288824	−	0.500257i	0.973529	+	0.228562i	$0.0734025\pi$
$972$		0			0
$973$	2.00000	+	10.3923i	0.0641171	+	0.333162i
$974$	25.0000			0.801052
$975$		0			0
$976$	0.500000	−	0.866025i	0.0160046	−	0.0277208i
$977$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$977$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$978$		0			0
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$	−2.00000	+	13.8564i	−0.0638877	+	0.442627i
$981$		0			0
$982$	−4.00000	+	6.92820i	−0.127645	+	0.221088i
$983$	2.00000	−	3.46410i	0.0637901	−	0.110488i	−0.832367	−	0.554226i	$-0.813015\pi$
$983$	2.00000	−	3.46410i	0.0637901	−	0.110488i	0.896157	+	0.443738i	$0.146348\pi$
$984$		0			0
$985$	24.0000			0.764704
$986$	−16.0000	+	27.7128i	−0.509544	+	0.882556i
$987$		0			0
$988$	12.5000	−	12.9904i	0.397678	−	0.413279i
$989$	−7.00000	−	12.1244i	−0.222587	−	0.385532i
$990$		0			0
$991$	−22.5000	−	38.9711i	−0.714736	−	1.23796i	−0.963061	−	0.269282i	$-0.913213\pi$
$991$	−22.5000	−	38.9711i	−0.714736	−	1.23796i	0.248325	−	0.968677i	$-0.420120\pi$
$992$		0			0
$993$		0			0
$994$	4.00000	+	20.7846i	0.126872	+	0.659248i
$995$	7.00000	+	12.1244i	0.221915	+	0.384368i
$996$		0			0
$997$	19.0000			0.601736			0.300868	−	0.953666i	$-0.402724\pi$
$997$	19.0000			0.601736			0.300868	+	0.953666i	$0.402724\pi$
$998$	12.5000	+	21.6506i	0.395681	+	0.685339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.b.1621.1	yes	2
3.2	odd	2		1638.2.m.d.1621.1	yes	2
7.2	even	3		1638.2.p.e.919.1	yes	2
13.3	even	3		1638.2.p.e.991.1	yes	2
21.2	odd	6		1638.2.p.b.919.1	yes	2
39.29	odd	6		1638.2.p.b.991.1	yes	2
91.16	even	3	inner	1638.2.m.b.289.1	✓	2
273.107	odd	6		1638.2.m.d.289.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.m.b.289.1	✓	2	91.16	even	3	inner
1638.2.m.b.1621.1	yes	2	1.1	even	1	trivial
1638.2.m.d.289.1	yes	2	273.107	odd	6
1638.2.m.d.1621.1	yes	2	3.2	odd	2
1638.2.p.b.919.1	yes	2	21.2	odd	6
1638.2.p.b.991.1	yes	2	39.29	odd	6
1638.2.p.e.919.1	yes	2	7.2	even	3
1638.2.p.e.991.1	yes	2	13.3	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.00000 - 1.73205i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-3.50000 - 0.866025i) q^{13} +(2.50000 + 0.866025i) q^{14} +1.00000 q^{16} +4.00000 q^{17} +(-2.50000 + 4.33013i) q^{19} +(1.00000 + 1.73205i) q^{20} +(1.00000 + 1.73205i) q^{22} +2.00000 q^{23} +(0.500000 - 0.866025i) q^{25} +(3.50000 + 0.866025i) q^{26} +(-2.50000 - 0.866025i) q^{28} +(4.00000 - 6.92820i) q^{29} -1.00000 q^{32} -4.00000 q^{34} +(-1.00000 - 5.19615i) q^{35} +7.00000 q^{37} +(2.50000 - 4.33013i) q^{38} +(-1.00000 - 1.73205i) q^{40} +(5.00000 - 8.66025i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(-1.00000 - 1.73205i) q^{44} -2.00000 q^{46} +(6.00000 + 10.3923i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-3.50000 - 0.866025i) q^{52} +(3.00000 - 5.19615i) q^{53} +(2.00000 - 3.46410i) q^{55} +(2.50000 + 0.866025i) q^{56} +(-4.00000 + 6.92820i) q^{58} +(0.500000 - 0.866025i) q^{61} +1.00000 q^{64} +(-2.00000 - 6.92820i) q^{65} +(4.00000 + 6.92820i) q^{67} +4.00000 q^{68} +(1.00000 + 5.19615i) q^{70} +(4.00000 + 6.92820i) q^{71} +(-4.50000 + 7.79423i) q^{73} -7.00000 q^{74} +(-2.50000 + 4.33013i) q^{76} +(1.00000 + 5.19615i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-5.00000 + 8.66025i) q^{82} +14.0000 q^{83} +(4.00000 + 6.92820i) q^{85} +(3.50000 + 6.06218i) q^{86} +(1.00000 + 1.73205i) q^{88} -6.00000 q^{89} +(8.00000 + 5.19615i) q^{91} +2.00000 q^{92} +(-6.00000 - 10.3923i) q^{94} -10.0000 q^{95} +(-8.50000 - 14.7224i) q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8} - 2 q^{10} - 2 q^{11} - 7 q^{13} + 5 q^{14} + 2 q^{16} + 8 q^{17} - 5 q^{19} + 2 q^{20} + 2 q^{22} + 4 q^{23} + q^{25} + 7 q^{26} - 5 q^{28} + 8 q^{29} - 2 q^{32} - 8 q^{34} - 2 q^{35} + 14 q^{37} + 5 q^{38} - 2 q^{40} + 10 q^{41} - 7 q^{43} - 2 q^{44} - 4 q^{46} + 12 q^{47} + 11 q^{49} - q^{50} - 7 q^{52} + 6 q^{53} + 4 q^{55} + 5 q^{56} - 8 q^{58} + q^{61} + 2 q^{64} - 4 q^{65} + 8 q^{67} + 8 q^{68} + 2 q^{70} + 8 q^{71} - 9 q^{73} - 14 q^{74} - 5 q^{76} + 2 q^{77} - 8 q^{79} + 2 q^{80} - 10 q^{82} + 28 q^{83} + 8 q^{85} + 7 q^{86} + 2 q^{88} - 12 q^{89} + 16 q^{91} + 4 q^{92} - 12 q^{94} - 20 q^{95} - 17 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8 - 2 * q^10 - 2 * q^11 - 7 * q^13 + 5 * q^14 + 2 * q^16 + 8 * q^17 - 5 * q^19 + 2 * q^20 + 2 * q^22 + 4 * q^23 + q^25 + 7 * q^26 - 5 * q^28 + 8 * q^29 - 2 * q^32 - 8 * q^34 - 2 * q^35 + 14 * q^37 + 5 * q^38 - 2 * q^40 + 10 * q^41 - 7 * q^43 - 2 * q^44 - 4 * q^46 + 12 * q^47 + 11 * q^49 - q^50 - 7 * q^52 + 6 * q^53 + 4 * q^55 + 5 * q^56 - 8 * q^58 + q^61 + 2 * q^64 - 4 * q^65 + 8 * q^67 + 8 * q^68 + 2 * q^70 + 8 * q^71 - 9 * q^73 - 14 * q^74 - 5 * q^76 + 2 * q^77 - 8 * q^79 + 2 * q^80 - 10 * q^82 + 28 * q^83 + 8 * q^85 + 7 * q^86 + 2 * q^88 - 12 * q^89 + 16 * q^91 + 4 * q^92 - 12 * q^94 - 20 * q^95 - 17 * q^97 - 11 * q^98

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